Suppose that identical duopoly firms have constant marginal costs of $16 per unit. Firm 1 faces a demand function of 9, = 100 - 2p, + 1p2. where q, is Firm 1's output, p, is Firm 1's price, and p, is Firm 2's price. Similarly, the demand Firm 2 faces is 92 = 100 - 2p2 + 1p,. Solve for the Bertrand equilibrium. In equilibrium, p, equals $ 44 and p2 equals $ 44. (Enter numeric responses using integers.) At these prices, q1 equals and q2 equals The total quantity supplied is.
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- Two firms - firm 1 and firm 2 - share a market for a specific product. Both have zero marginal cost. They compete in the manner of Bertrand and the market demand for the product is given by: q = 20 − min{p1, p2}. 1. What are the equilibrium prices and profits? 2. Suppose the two firms have signed a collusion contract, that is, they agree to set the same price and share the market equally. What is the price they would set and what would be their profits? For the following parts, suppose the Bertrand game is played for infinitely many times with discount factor for both firms δ ∈ [0, 1). 3. Let both players adopt the following strategy: start with collusion; maintain the collusive price as long as no one has ever deviated before; otherwise set the Bertrand price. What is the minimum value of δ for which this is a SPNE. 4. Suppose the policy maker has imposed a price floor p = 4, that is, neither firm is allowed to set a price below $4. How does your answer to part 3 change? Is it now…. The market for widgets consists of two firms that produce identical products. Competition in the market is such that each of the firms independently produces a quantity of output, and these quantities are then sold in the market at a price that is determined by the total amount produced by the two firms. Firm 2 is known to have a cost advantage over firm 1. A recent study found that the (inverse) market demand curve faced by the two firms is P = 280 – 2(Q1 + Q2), and costs are C1(Q1) = 3Q1 and C2(Q2) = 2Q2. a. Determine the marginal revenue for each firm. b. Determine the reaction function for each firm.What is the homogeneous-good duopoly Cournot equilibrium if the market demand function is Q=4,000-1,000p, and Firm l's and Firm 2's variable cost functions are V (q1) = 0.22qlandV (q2) = 0.22q2 , respectively. Select one alternative: Both firms produce 1300 units of outpuit. Both firms produce 1280 units of output. Both firms produce 1240 units of output. Both firms produce 1260 units of output.
- Two firms compete in selling homogeneous goods. They choose their output levels q1 and q2 simultaneously and face demand curve P=80-6Q, where Q=q1+q2. The total cost function of firm 1 is C1=8q1 and the total cost function of firm 2 is C2=32q2+2/3. a) Find and draw the reaction curves of the two firms. b) Compute equilibrium quantities, price and profits. Suppose now that firm 2, thanks to a technological innovation, becomes more efficient. The new total cost function of firm 2 is C2=8q2 c) Compute the new equilibrium quantities, price and profits.Suppose that identical duopoly firms have constant marginal costs of $16 per unit. Firm 1 faces a demand function of 9, = 100 - 2p, + 1p2, where q, is Firm 1's output, p, is Firm 1's price, and p, is Firm 2's price. Similarly, the demand Firm 2 faces is 92 = 100 - 2p2 + 1p1. Solve for the Bertrand equilibrium. In equilibrium, p, equals $ and p2 equals $. (Enter numeric responses using integers.)Consider two firms that produce the same good and compete setting quantities. The firms face a linear demand curve given by P (Q) = 1 − Q, where the Q is the total quantity offered by the firms. The cost function for each of the firms is c(qi) = cqi, where 0 < c < 1 and qi is the quantity offered by the firm i = 1,2. Find the Nash equilibrium output choices of the firms, as well as the total output and the price, and calculate the output and the welfare loss compared to the competitive outcome. How would the answer change if the firms compete setting prices? What can we conclude about the relationship between competition and the number of firms?
- Suppose that there are two firms operating in the market of laptops, the first firm supplies quantity qi and the second firm supplies q2. The inverse demand function for laptops is P(q1 +q2)=2,000-2(q₁ +q2). The marginal costs are constant and equal to $400. a. b. c. Find the Cournot equilibrium outputs and price. Find the Bertrand equilibrium outputs and price. Suppose that the first firm is the leader choosing the output first, and the second firm is the follower choosing the output after observing the firm firm's choice. Find the new equilibrium output and price and compare them with those in parts a and b. Which of the equilibria is socially preferable?Consider two firms that provide a differentiated product, which they produce at the same constant marginal cost, MC = 3. The demand function for Firm 1 is q1 = 10 - p1-0.5p2 and for Firm 2 is q2 = 20 - p2 - 0.5p1, where p1 is Firm 1's price and p2 is Firm 2's price. What are the Nash-Bertrand equilibrium prices and quantities? If the two firms merged, what would be the new equilibrium prices and quantities, and how would they compare to the pre-merger prices?Solve for the Bertrand equilibrium for the firms described below if Firm 1's marginal cost is $15 per unit and Firm 2's marginal cost is $25 per unit. Firm 1 faces a demand function of 91 = 140 – 2p, + 1p2, where 91 is Firm 1's output, p, is Firm 1's price, and p, is Firm 2's price. Similarly, the demand Firm 2 faces is 92 = 140 - 2p2 + 1p1. Solve for the Bertrand equilibrium. In equilibrium, p, equals and p2 equals (Enter numeric responses using integers.) At these prices, q, equals and 92 equals The total quantity supplied is
- Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm 1 faces a demand function of q1 = 70 – 2p1 + 1p2, where q, is Firm 1's output, p, is Firm 1's price, and p, is Firm 2's price. Similarly, the demand Firm 2 faces is 92 = 70 – 2p2 + 1p1- Solve for the Bertrand equilibrium. In equilibrium, p1 equals $ and P2 equals $ (Enter numeric responses using integers.)Suppose there are just two firms, 1 and 2, in the oil market and the inverse demand for oil is given by P = 60 – Q. The marginal cost for each firm is €30. What price should Firm 2 charge at the Cournot equilibriumTwo firms sells an identical product. The demand function for each firm is given: Q = 20 - P, where Q = q1 + q2 is the market demand and P is the price. The cost function for reach firm is given: TCi = 10 + 2qi for i = 1, 2. a) If these two firms collude and they want to maximize their combined profit, how much are the market equilibrium quantity and price? b) If these two firms decide their production simultaneously, how much does each firm produce? What is the market equilibrium price? c) If Firm 1 is a leader who decides the production level first and Firm 2 is a follower, how much does each firm produce? What is the market equilibrium price?